The transmission ellipsometric function (TEF) of a film-substrate system relates the polarization change, upon transmission, of an electromagnetic wave obliquely incident on, and transmitted through, a film-substrate system. The behavior of the TEF depends on the category of the film-substrate system: negative, zero, or positive. The category is determined by the sign of  N_1-\sqrt{N_0{N}_2} : negative for a negative film-substrate system, zero for a zero system, and positive for a positive system. We discuss the behavior of the TEFs of the two transparent nonnegative film-substrate systems, zero and positive. We describe the TEF as two successive transformations and analyze its behavior as the angle of incidence and film thickness of the film-substrate system are changed. We use the constant-angle-of-incidence contours and constant- thickness contours to analyze and utilize that behavior. From the analysis and understanding of the behavior of the TEF, and from the definition of a polarization device as a film-substrate system that introduces prescribed polarization changes, we discuss the design of all possible types of polarization devices using either of the two systems. We present a design formula for each. We also present a general formula that is used for the design of any of the devices. Thin-film coatings are treated as polarization devices for the purposes of our discussion. We conclude with a brief discussion of suggested practical modifications to, and simplifications of, ellipsometric memory, which is an interesting application of polarization devices for which there is a patent pending.